I'm going to give you a LIKE for your first sentence! If I could, I would give you 10, I'd give you another 10 for, "003 is only going to improve on the J-15's abilities"!
well stated, it then is a bit of a mystery why we aren't seeing more J-15s in production? lack of aircrew is most certainly not the reason? hopefully at some point someone will actually "fill in the blanks" for us, but I do expect to see a healthy number of J-15's on Chinese carriers for the foreseeable future, just as the USN will continue to support and fly the Super Hornet!
Honestly my guess is production was paused due to program timing. Consider these things:
1. PLAN only had one working carrier in service and would only have one for many years. The second carrier is based off the Varyag as well but with further modification on top of 001's. These modifications were made based on the lessons learned from both sea ops and operating the J-15. So at most PLAN will have two operable carriers for at least a decade from 001 in service until 003 in service. This is quite a long time for a fighter development to stay static. Having only two carriers with fighters custom "designed" for them, there isn't much point building a whole bunch when you will need to upgrade those fighters soon and while you're upgrading them you would also be tailoring them to the 003 and future carriers.
2. There seemed to be some problems with the flight control. You don't want to build a hundred fighters with a known problem without resolving it first.
3. J-11B receiving upgrades while J-15 seems to also desperately need a modernisation. It came out seemingly more lacking at least in the radar department despite PLAAF's fighters featuring higher end electronics during the same time period. This could be because more time and effort was required to make the fighter carrier capable and corrosion resistant.
I think these things point towards PLAN waiting for a "J-15G" which solves the FCS issue, receives comprehensive upgrades (also to network with future naval assets like AWACS and drones), is more tailored for 003 (landing + CATOBAR), and features WS-10H if it becomes ready. Even though WS-10 variants have proven remarkable reliability after nearly 10 years of service without issue and CAC is comfortable enough with it on their single engined baby, corrosion and operating it in a carrier environment is a totally different set of engineering challenges and who knows when the H variant will become reliable enough for PLAN to bet everything on. One oversight and the whole fleet will need engine replacements.
There are quite a few things it would be waiting for depending on how desperately PLAN needs them ready but the development timing will almost definitely align with 003. So we'll need to watch 003 to really know when to expect a new J-15.